Numerical investigations of the concrete pouring process and the void distribution in the steel−concrete−steel structure: The Shenzhong Link, China

Abstract

The steel-shell concrete immersed tube (SSIT) with the self-compacting concrete (SCC) has been applied in the Shenzhen–Zhongshan Link, and the SSIT is prone to the void defect during the concrete pouring process. This work aims to study the flow behavior of the SCC and investigate the generation and distribution of the void defect in the SSIT, and the computational fluid dynamics (CFD) models are adopted to solve the above problems. To verify the CFD models, the slump test, L-box test, and field test based on Ok. the impact image method are carried out. The effects of the connecting hole spacing, the exhaust hole number, the exhaust hole position and the pouring speed on the flow behavior and the void defects distribution are quantitatively compared. According to the comparison results, the standard compartment with 300 mm connecting hole spacing and 10 exhaust holes is the optimal compartment structure design, and the concrete pouring speed of 15 m³/h is the optimal construction method. This work demonstrates that the CFD model offers a useful way to evaluate the generation and distribution features of the void defects for the steel–concrete–steel structure.

Graphical abstract

Keywords

Shenzhen–Zhongshan Link / self-compacting concrete / flow behavior / distribution the void defects / computational fluid dynamics

1 Introduction

The Shenzhen–Zhongshan Link is the longest and largest full sandwich steel−concrete immersed tube tunnel made of bridge, island, tunnel, and underground communication. The design schemes of the Shenzhen–Zhongshan Link are divided into two parts as follows. On the west side the bridge with a length of 17.19 km is construct, and immersed tunnel with a length of 6.72 km on the east side. The immersed tunnel consists of 32 tunnel elements, as described in Fig.1. The typical element is 165.0 m long, 46.0 m width and 10.6 m high shown in Fig.2(a). The tunnel element is comprised of the steel–concrete–steel (SCS) sandwich structure. The SCS structure typically consists of a sandwiched concrete core connected to two external steel plates using mechanical shear connectors [1,2], as shown in Fig.2(c) and Fig.2(d). Among them, the inner and outer plates are the main bending members, and the transverse mediastinum plates are the main shear members, which connects the inner and outer panels to form a force whole. The longitudinal stiffeners are made of T-shaped steel ribs and angle steel, which are mainly used as shear connectors to ensure effective connection between the steel plate and concrete. A pouring hole with a diameter of 273 mm and 10 exhaust holes with a diameter of 92 mm are reserved on the compartment.

The SCS structure behaves good performance in terms of high flexural stiffness and energy absorption capacity to withstand extreme environmental and accidental loads [3]. The SCS structure is filled with self-compacting concrete (SCC), and the void defects are unavoidable in the steel−concrete interface [4]. The presence of these void defects may significantly influence the mechanical properties in relation to the bond strength between the concrete core and faceplates and composite action of the structure [5,6]. Therefore, it is necessary to understand the flow characteristics of the fresh concrete in the SCS structure and the resistance effect from mechanical shear connectors to further reveal the formulation and distribution features of the void defect for the SCS structure.

In recent times, some investigations have been conducted into the distribution feature of the void defect with a variety of approaches, for instance, non-destructive testing techniques [7,8], laboratory investigation methods [9,10], and the numerical methods [11,12]. Compared with the non-destructive testing technique and experimental methods, numerical methods have enjoyed significant popularity to study the flow behavior of the SCC, due to their time and cost efficiency [13]. In general, the numerical methods are grouped into three types: the discrete element method (DEM) [14–17], the computational fluid dynamics (CFD) method [18,19] and the coupling method [20]. In DEM, mortar and aggregate are represented by particles, and the rheological property of SCC is reflected by the contact model between particles. It has been found a wide application in modeling the flow capacity of the SCC. Nevertheless, there are some aspects that need to be strengthened in this method. For example, the contact force and viscosity coefficient between particles lack a clear physical meaning. An alternative method is the CFD method, in which all the phases are treated as fluid, and the contact interactions and strong coupling between different phases can be avoided. However, the SCC has been considered as two-phase materials composed of aggregate particles dispersed in a cement paste matrix. The rheological properties are naturally determined by the rheology of the matrix and the volume content of coarse aggregate. Therefore, the recent advances in the numerical modeling have a significative attempt in the combination of the CFD and the DEM. The key challenge is the description of the fluid−solid moving interfaces. Currently, the coupled models are still in its infancy and suffers from the inefficiency and incomplete theory. Since the work focuses on the flow-diffusion process of the fresh concrete and discharge or air accumulation blocked by steel plates and shear connectors in the closed compartment, moreover, the flow characteristics and relative motion of the material components of the SCC are not considered, the CFD method is adopted in this work to simulate the pouring of the SCC.

In essence, the SCS structure also exhausts air while pouring concrete. Thus, it is a straightforward choice to use the two-phase flow model to simulate the pouring process of SCC. SCC is generally described by using the Bingham model, modified Bingham model, or Herschel-Bulkley model [21–23]. The flow behavior of the SCC and air is simulated by the Navier−Stokes Equations [24]. When using the two-phase flow model, a conservative interface representing method becomes a key issue for accurately depicting the free surface between concrete and air. Typical methods of capturing the free surface include the Volume of Fluid (VOF) method [25] and the Level Set method (LS) [26]. The LS method has been considered as a simple and efficient numerical tool to mark the free surface directly with the distance signed function [13]. However, the mass conservation cannot be preserved when advecting and re-initializing the indicator function [27]. On the other hand, the VOF method, based on the Marker and Cell method, is widely used transient surface-tracking method designed for two-phase or multiphase flows. In the VOF method, a single set of mixture momentum and energy equations is shared among all the phases, and the interface is captured by a color function that tracks the volume fraction occupied in each element [28]. Compared with the LS method, the VOF method has excellent mass conservation, which ensures conservation of the volume of each fluid type in the system [29].

This work focuses on the SCC pouring and filling process of SCS structures. Therefore, the two-phase flow model is applied to simulate the flow behavior of SCC and predict the pouring quality. Additionally, SCC is described using Bingham model, and the interface between SCC and air is tracked by the VOF method. On this basis, the influence of the spacing between the connecting holes, the study examines the influence of factors such as the spacing between connecting holes, the number of exhaust holes, their positions, and pouring speed on the quality of SCC pouring. Meanwhile, a comparison and summary of the depth and distribution of void defects under different conditions are provided to optimize the design and construction scheme of SCS structures. The paper is organized as follows. In Section 2, the basic idea of the numerical schemes is first introduced briefly followed by the constitutive model and the measurement of the rheological parameters in Section 3. In Section 4, the numerical model and simulation schemes are introduced detail. Subsequently, the flow behavior of the fresh concrete in the compartment of Shenzhen–Zhongshan link is analyzed, while the formulations and distribution characteristics of fresh concrete would be discussed. At the end of this paper, conclusions are provided in Section 6.

2 Theoretical methods

2.1 Rheological model

According to the research results of Tattersall and Banfill [30], the Bingham fluid could reflect the rheological behavior of fresh concrete. The Bingham fluid behaves as an elastic solid before the external force reach its yield stress, while behaves as a fluid when the external force exceeds its yield stress. The Bingham rheological model describes the shear behavior of fluid through two rheological parameters: yield stress τ₀ and plastic viscosity μ. The rheological model could be represented by:

(1)\{\begin{array}{ll}\tau =G\cdot \gamma ,& \text{if}\tau \le {\tau }_0,\\ \tau ={\tau }_0+\mu \cdot {\gamma }^{\mathrm{\prime }},& \text{if}\tau >{\tau }_0,\end{array}

where τ, G, \gamma, and {\gamma }^{\mathrm{\prime }} are shear stress, fluid elastic constant, shear deformation, and shear rate, respectively.

2.2 Volume-of-fluid method

2.2.1 Theoretical framework

The VOF method assumes that the fluids are immiscible. When a fluid is added to the calculation domain, its volume fraction is introduced as a new variable (the sum of the volume fractions of all fluids within the domain is equal to 1. Through defining the volume fraction of each fluid within the CFD cell, the VOF method could capture the interface between different fluids. Taking the two-phase flow (fluid A and fluid B) as an example, a CFD cell within the calculation domain may contain only one fluid or it may be a mixture of two fluids, depending on the volume fraction of the fluid (α_A and α_B), as shown in Fig.3.

After determining the CFD cells where the fluids and the interface are located, it is necessary to reconstruct the interface in the CFD cells, that is, to approximate the interface section in each cell. In the VOF method, two common interface reconstruction methods are the simple line Interface calculation method (SLIC) [31] and the piecewise linear interface calculation method (PLIC) [32]. The SLIC method is the simplest interface reconstruction method, and the interfaces are determined through the volume fractions and a series of line segments parallel to the cells, as shown in Fig.4(a). The PLIC method is relatively precise, and the interfaces are determined through the volume fractions and the normal vectors of the interface sections, as shown in Fig.4(b), so in this work, the PLIC method is adopted.

2.2.2 Governing equations

In the VOF method, the fluid motion is controlled by mass conservation (the continuity equation) and momentum conservation (the motion equation).

To track the interface between the fluids, the continuity equations of the volume fractions of the fluids are solved. For the fluid A, the continuity equation is given by:

(2)\frac{1}{{\rho }_A}\left[\frac{\mathrm{\partial }}{\mathrm{\partial }t}\left({\alpha }_A{\rho }_A\right)+\mathrm{\nabla }\cdot \left({\alpha }_A{\rho }_A{\mathit{v}}_A\right)=S_{{\alpha }_A}+\sum _{B=1}^n\left(m_{BA}-m_{AB}\right)\right],

where ρ_A, α_A, v_A, S_{{\alpha }_A} are the density, volume fraction, velocity, and mass source term of the fluid A, respectively, m_{BA} is the mass transfer from fluid B to fluid A, m_{AB} is the mass transfer from fluid A to fluid B.

The motion equation is solved throughout the calculation domain, and the velocity field is shared among the fluids. The motion equation depends on the volume fractions of all fluids, which could be written as:

(3)\{\begin{array}{rl}& \frac{\mathrm{\partial }}{\mathrm{\partial }t}\rho \mathit{v}+\mathrm{\nabla }\cdot (\rho \mathit{v}\mathit{v})=-\mathrm{\nabla }p+\mathrm{\nabla }\cdot \left[\mu \left(\mathrm{\nabla }\mathit{v}+\mathrm{\nabla }{\mathit{v}}^T\right)\right]+\rho \mathit{g}+\mathit{F},\\ & \rho =\sum _{A=1}^n{\alpha }_A{\rho }_A\stackrel{\mathrm{t}\mathrm{w}\mathrm{o}\text{-}\mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}{\to }\rho ={\alpha }_A{\rho }_A+\left(1-{\alpha }_A\right){\rho }_B,\\ & \mu =\sum _{A=1}^n{\alpha }_A{\mu }_A\stackrel{\mathrm{t}\mathrm{w}\mathrm{o}\text{-}\mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}{\to }\mu ={\alpha }_A{\mu }_A+\left(1-{\alpha }_A\right){\mu }_B,\end{array}

where ρ and μ are volume-fraction-averaged density and viscosity, respectively, p is the pressure, v is the velocity, g is the gravitational acceleration, and F is a source term which relates to the surface tension.

In this work, the continuum surface force model [33] is applied to calculate the surface tension. The surface tension could be represented by pressure jumps on the surface, and the force at the surface could be written as a volume force through divergence theorem:

(4)

where σ_AB is the surface tension between fluids A and B, \kappa is the curvature defined by the divergence of unit normal.

3 Calibration and verification

In this section, the “Fifty-cent rheometer” method [34] is applied to preliminarily estimate the yield stress of SCC. According to the procedure presented in Ref. [34], Eq. (5) shows the relation between the yield stress and the final expansion radius of the SCC:

(5){\tau }_0=\frac{225\rho g{\mathrm{\Omega }}^2}{128{\text{π}}^2{R}^5},

where τ₀ is the yield stress, ρ is the density, g is the gravitational acceleration, Ω is the volume, and R is the final expansion radius. In this study, the parameters in Eq. (5) are determined according to the parameters of the SCC test, as described in Tab.1, and the mix design of the SCC is presented in Tab.2. The parameters used in this work are ρ = 2300–2350 kg/m³, g = 9.81 m/s², Ω = 0.00175π m³, R = 0.305–0.350 m, and the preliminary estimated yield stress value of the SCC is 23.13–47.02 Pa.

Finally, leveraging the data obtained from the slump test and L-box test, the viscosity coefficient of SCC is accurately determined through the inverse analysis.

3.1 Slump test

The slump test is a traditional testing method to assess the rheological properties of the SCC, and it is also the main means to check whether the SCC workability meets the requirements. Thus, the slump test is selected to verify the validity of the CFD method and preliminarily calibrate the parameters.

In the slump test, the concrete is filled with the slump cone at one time, without vibration or compaction during the whole process. Then, the slump cone is lifted vertically within 5 s, and the concrete flows freely until reaches the steady-state. In the numerical simulation, the SCC model is first filled in the slump cone model, and then the SCC model diffuses under the action of gravity. When the flow rate of SCC remained basically unchanged, the final expansion diameter of the SCC model is measured and compared with the test results. As shown in Fig.5, the final expansion diameter of the numerical simulation is close to that of the SCC in the test, which are 647.2 and 650.0 mm, respectively. It illustrates good agreement between the simulation result obtained by the CFD method measurement from the slump test. Therefore, the parameters preliminarily are proposed as: ρ = 2400 kg/m³, τ₀ = 35 Pa, and μ = 20 Pa·s.

3.2 L-box test

The L-box test could be used to evaluate the passing ability of SCC. In this section, the same SCC is adopted for test, and the process is simulated by the CFD method as those in Subsection 3.1 to further check the parameters.

In the L-box test, the SCC is poured in the vertical channel. After the pouring is completed, the sliding door is lifted vertically. Then the SCC passes through the steel bars and enters the horizontal channel. In the numerical simulation, the SCC is first filled in the vertical channel of the L-box model, and when the calculation starts, the SCC model flows along the horizontal channel until the velocity reaches a stable state.

Based on the L-box test and its numerical simulation results, the flow of the SCC at different positions are compared, as presented in Fig.6. The comparison results demonstrate a basic consistency between the flow distances and liquid surface lines in the SCC model and those observed in the actual test. The above comparison results show that the SCC model used in this study could simulate the rheological behavior of real SCC accurately, which further proves the accuracy of the parameters and the applicability of the CFD method (as shown in Tab.3).

3.3 Field test

To preliminarily judge the position of the void defects and verify the rationality of the numerical simulation results, the impact image method is adopted in this study to detect the positions and depths of the void defects in the standard compartment [9].

In Fig.7(a), the distribution of the void area with a depth greater than 2 mm achieved by the experiment test is exhibited. The void area is mainly concentrated around the pouring holes, the T-shaped steel ribs, and the walls of Parts II–IV. For comparison, the test was also simulated by the CFD. In Fig.7(b), the volume fraction of SCC near the pouring holes and T-shaped steel ribs changes significantly. It is possible to observe that the simulation results are basically consistent with the experimental results. In addition, it could be noticed that the experimental results are affected by the accuracy of the equipment and the void area with a depth of less than 2 mm cannot be identified. The numerical method provides a more comprehensive view. It can reflect the distribution characteristics of the void defects with different depths.

4 Numerical model and simulation schemes

4.1 Geometric modeling and meshing

Based on the scheme of the Shenzhen–Zhongshan Link, the steel compartments are modeled. Taking the standard compartment as an example, the numerical model and its geometric dimensions are shown in Fig.8(a). The compartment is marked with five parts (Parts I–V) according to the positions of the four T-shaped steel ribs, as presented in Fig.8(a). The model of the standard compartment is divided into 1129824 elements, and the element size ranges from 1.3 to 102.55 mm. The specific meshing elements and boundary conditions are shown in Fig.8(b). In the CFD calculations, the concrete pouring speed is uniformly set to 20 m³/h.

4.2 Numerical simulation schemes

The work focuses on the investigation of the effects of the structural form and construction method on the flow behavior of the SCC, therefore, the simulations are designed with 4 cases as follows.

Case 1: Spacing between the connecting holes. This case comprises two models with the identical geometric dimensions (excluding the T-shaped steel ribs) and the exhaust hole distribution. The spacing between the connecting holes is 300 mm in Model A (Fig.9 (a)) and 500 mm in Model B (Fig.9(b)).

Case 2: Number of the exhaust holes. This case involves three models with the same geometric dimensions and the connecting hole spacing (300 mm). The number of the exhaust holes of Model C (Fig.10(a)), D (Fig.10(b)) and A (Fig.10 (a)) is 4, 8, and 10, respectively.

Case 3: Position of the exhaust holes. This case includes four models with the same geometric dimensions and the connecting hole spacing (300 mm). The sizes and positions of the exhaust holes of Model A, E, F, and G are shown in Fig.9(a), Fig.11(a), Fig.11(b), and Fig.11(c), respectively.

Case 4: Pouring speed. In this case, the standard compartment model (Model A) is used to compare the effects of concrete pouring speeds of 15 m³/h (Condition A), 20 m³/h (Condition B), and 40 m³/h (Condition C) on the pouring quality and the distribution of the void defects.

5 Results and discussions

The following part describes the simulation results for the flow behavior of the SCC in different cases. First, the simulation for the effect of structural design of the compartment, for instance the spacing between the connecting holes, as well as the number and positioning of the exhaust holes, on the concrete pouring and filling quality of the SCS structure is simulated. Afterwards, the influents associated with the pouring speed is discussed. In the work, a monitoring point (750 mm width × 875 mm length × 1495 mm height) is selected to record the velocity of the fluid in the compartment. Meanwhile, the zone with SCC volume fraction less than 0.5 is defined as the void defects, and the distributions of SCC at specific depths (1, 2, 3, and 5 mm) are also discussed. The determination of the simulation termination time is dependent upon the actual casting plan, specifically, it halts when the concrete interface within the vent reaches a height of 1000 mm.

5.1 The spacing between the connecting holes

This section provides the results of a study on the influence of the spacing between the connecting holes on the SCC pouring and filling quality. Both the events show the similar characteristics of flow behavior of the SCC and distribution of void defects. The free surface of the SCC in the compartment is gradually rising, along with the continuous injection of the SCC. The air is disturbed and triggered under the effect of the concrete, and gathers to the exhaust holes through the connecting holes in the T-shaped steel ribs and other areas forming a regular exhaust channel. Finally, the air is discharged through the exhaust pipes. However, little air is blocked by the connecting parts, and accumulates near the connecting hole and the exhaust hole resulting in void areas.

Fig.12 shows the time-flow velocity curve of the monitoring point and the streamline diagram of the compartments with different connecting hole spacing. All flow rate monitoring points are located at the connecting hole, and thus the velocities can reflect the fluid flow velocity at the connecting hole. Shown in this figure, velocity of the monitoring point increases rapidly before the free liquid surface height reaches 1.498 m at 12 s, because of the gradually increasing air pressure. Subsequently, the surface exceeds the monitoring point, while the flow velocity gradually decreases and tends to be within the stable range. The peak velocities of Model A and Model B are 0.52 and 0.48 m/s, respectively. Compared to Model B, the connecting hole spacing in Model A is smaller and the flow velocity at the monitoring point is higher, which is more conducive to the discharge of air and the filling of SCC.

The void area percentage of the compartments with different connecting hole spacings is presented in Fig.13. From the results, the void zones of Model A and Model B are concentrated within the depths of 1 and 2 mm, respectively. In particular, the percentage of void area in Model A decreases 76.23% with depth varied from 1 to 2 mm, whereas the percentage further reduce to 0.84% and 0.43% at depth 3 and 5 mm. In contrast, Excessive connecting hole spacing in Model B results in the poor fluidity of the internal air and diffusion degree of the concrete, which significantly aggravates the cavitation problem near the T-shaped steel ribs and the wall in Part III. In Model B, the void area percentage remains high at 66.89% at a depth of 2 mm. At deeper levels of 3 and 5 mm, the percentages are 3.59% and 2.19%, respectively. These values are significantly higher compared to those in Model A. It is clearly that the small connecting hole spacing reduces the accumulation of air, and significantly inhibits the propagation of the void area in the depth direction. Furthermore, compared with Model B, the liquidity of different parts in Model A is improved, namely, more air can be discharged from the compartment through the connecting hole, resulting in higher pouring quality of SCC in different parts especially the local area near the T-shaped steel ribs.

In summary, the fluid flow in Model A is faster than that in Model B which is conducive to the filling of SCC, and the void zone is also smaller. Thus, the design scheme with a spacing of 300 mm between the connecting holes is better than that with a spacing of 500 mm.

5.2 The number of the exhaust holes

In this section, the effect of the number of the exhaust holes on the pouring and filling quality of SCC is analyzed. The velocity curve of the monitoring point is exhibited in Fig.14. The velocity increases following the increment of the number of exhaust holes. In this detailed description of the test, the velocity in Model C is much lower than that in Model A and Model D. Additionally, the lagging peak velocity in Model C indicates low liquidity. Thus, Model C exhibits design defects. Specifically, the gas circulation within the compartment is poor, resulting in more gas accumulation in the parts without exhaust holes.

Fig.15 shows the void area percentage of the compartments with different numbers of the exhaust holes. The void problem caused by the exhaust holes can be observed clearly. In Model C, low liquidity and insufficient air discharge channel result in serious void phenomenon, due to the lack of exhaust holes in Parts II–IV. The void area percentage in Model C remained at 76.61% at the depth of 2 mm, and 2.59% and 1.51% at the depth of 3 and 5 mm, respectively. Therefore, void areas of Model C are concentrated within the range of 2 mm, which is higher than those in Model A and Model D. The SCC in Model A and Model D behave good compactness, and only a small amount of void areas are distributed near the T-shaped steel ribs and at the wall of Part III. In Model A and Model D, the void area percentage at the depth of 2 mm is 11.07% and 11.87%, respectively. However, it is worth noting that the external force acting on the fluid in Parts I and V is less than that in the other parts, since Parts I and V are far away from the pouring hole. If sufficient exhaust holes are not set in these parts, as shown in Model D, it could lead to the air accumulation and the generation of the void areas. Therefore, compared with Model C and D, the exhaust efficiency and SCC pouring quality of the compartment with 10 exhaust holes in Model A are optimal.

5.3 The position of the exhaust holes

This section provides the simulation results of model with different exhaust hole positions. The results are shown in Fig.16. From the results, the difference of the peak velocities among the models is not significant, and they occur at almost the same. The liquid exhibits a good fluidity for these models. Nevertheless, the velocity in Model G is smaller than that in other models. The main reason is owing to the reduction of effective exhaust channels caused by the unreasonable structural design.

The void area percentage of the compartments with different exhaust hole position is illustrated in Fig.17, and the void area percentages in different parts are summarized in Tab.4. It is worthwhile to notice that the void area of each model is within the range of 1 mm. Whereas, the movement and addition of the exhaust holes only affect the flow behavior of SCC in the part where the exhaust holes are located.

1) In Model E, the exhaust holes in Part I are set at its center to reduce the generation of the void area near the T-shaped steel ribs in Part I. However, the airflow retardation can also be observed around the T-shaped steel ribs. Moreover, it reduces the fluidity of the air in Part I, and the volume fraction of concrete grout is decreased in the zones around the wall of Part I.

2) In Model F, two exhaust holes with diameter of 42.4 mm are added in Part I and the exhaust holes in Part IV are moved to the T rib. It is clearly that the void area percentage reduces to 4.46% in Parts I and II which is lower than that in Model A, because of the addition of the exhaust holes. Moreover, due to the lack of the exhaust hole in Part IV and the long distance of the exhaust holes which is further away from Part III, the void area percentage has risen by 1.62% compared with that of Model A.

3) In Model G, the exhaust holes in Part II are moved on the top of the T-shaped steel rib, in addition, the exhaust holes in Part IV are moved to Part V. The void area percentages are 10.14% and 24.78%, respectively. It is worthwhile to notice that the air content in each part of Model G is much higher than that in model A.

In summary, the problem of increased air content can occur where the position of the vent has changed, resulting in an increased void area inside the compartment along the T-shaped steel ribs. Compared with the standard compartment (Model A), the adjustment of the position of the exhaust hole does not improve the discharge of the air near the T-beam, but rather hinders the flow of gas/liquid. According to the calculation results, the pouring quality of the 4 models is Model G, Model F, Model E, and Model A in descending order. Therefore, in the design schemes of 10 exhaust holes, the SCC pouring and filling effect of Model A is the best.

In summary, the impact of the position of the exhaust holes on the SCC pouring and filling is only reflected in the Part where it is located. Among the different exhaust hole design schemes (all containing 10 exhaust holes), the fluid flow in Model A is the fastest and the void zone is the smallest. Thus, the exhaust hole position design of Model A (the standard compartment) is the most reasonable.

5.4 Investigation of the pouring speed

According to the research in the preceding sections, effects of different concrete pouring speeds on SCC void defects are discussed in this section. During this simulation, the standard model, namely, Model A is adopted. Fig.18 presents the velocity curve of the monitoring point in Model A under different concrete pouring speeds. The pouring speed has a direct impact on the fluid flow in the compartment. The higher the pouring speed, the higher the fluid velocity in the compartment and the faster the flow reaches a steady-state. The peak velocity of the monitoring points in Condition A, B, and C are 15, 20, and 40 m³/h, respectively, and the time required to reach a steady-state is approximately 10, 20, and 40 s, respectively.

Fig.19 presents the void area percentage of Model A under different SCC pouring speeds. At the depth of 2 mm, the void area percentage of Condition C reaches 34.71%, which is obviously higher than that of Condition A (13.36%) and Condition B (11.87%). It indicates that the void defects of Condition A and B are concentrated within the depth of 1 mm, while the void defects of Condition C are concentrated within the depth of 2 mm. Due to the minimum pouring speed in condition A, the free surface of the SCC rises slowly. As a result, the SCC is sufficiently self-leveling. Therefore, the void area in condition A is the smallest among these conditions. In contrast, the fluid block can be observed in condition C, and the area of the void defect increases in Parts II–IV.

Based on the distribution characteristics of the void region in the zones at depth of 2 mm, within a certain range, the higher the concrete pouring speed, the faster the fluid flow in the compartment, and the better the SCC filling quality. However, if the pouring speed is too high, the self-leveling efficiency of SCC decreases, leading to serious void defects and a decrease in pouring quality. Therefore, it is best to set the concrete pouring speed as 15 m³/h.

6 Conclusions

The numerical simulations in this work were aiming at investigating the flow behavior of the SCC and providing a basic technical support for predicting the formulation and distribution features of voids. In this work, the CFD model was introduced to solve above problems. The parameters used in this work verified and the performance of the model are validated by the experimental results and test result with the impact image method. During the current work, the Shenzhong link in Guangdong province, China, is taken as an example. The VOF method is applied to study the flow behavior of the concrete pouring process and the distribution of void defects in SCS. The effects of different factors on the filling quality of SCC in the compartment are compared and analyzed from the two aspects of the compartment structure design and construction method. The conclusions are summarized as follows.

1) The formulation of the voids can be owing to the restricted flow of concrete in the compartment and the accumulation of air. With an initial velocity, the concrete is driven by the gravity, and air is disturbed and triggered under the effect of the concrete. Due to the blocking effect of the shear connector, the air gathers around the T-rib plate forming the void zone. The distribution of the void zone is mainly distributed in the three cells in the middle of the compartment, namely the position near the T-rib plates on both sides of the pouring hole and the steel plates of the cells. The results are in good agreement with the test results.

2) The increase of the space of connecting holes reduces the fluidity in the middle three cells of the compartment. As a result, the phenomenon of air accumulation and voids is more prominent than that in the standard compartment.

3) The number of exhaust holes plays an important role in the formulation of the void. The design of four exhaust holes cannot meet the needs of the project, since there is a large area of air accumulation in the cell lacking the exhaust holes in the middle of the compartment. The simulated results of model with 8 exhaust holes are close to those of the standard case, nonetheless the void zone near the T-rib plates on both sides of the injected hole is larger than that in the standard compartment.

4) The location of the exhaust hole has a great influence on the generation and distribution of the void zones. Adding exhaust holes in a single cell can significantly improve the pouring quality of concrete in this cell. In addition, the exhaust hole arranged near the T-rib plate will affect the other side of the same cell that far away from the T-rib plate, resulting in air accumulation and void problems.

5) From the perspective of construction methods, appropriately increasing the concrete pouring speed could accelerate the fluid flow in the compartment and reduce the void defects, but an excessively high pouring speed will aggravate the void problem.

In summary, the standard compartment with 300 mm connecting hole spacing and 10 exhaust holes is the optimal compartment structure design, and the concrete pouring speed of 15 m³/h is the optimal construction method. It is worth noting that SCC consists of mortar and aggregates. For future research, the CFD–DEM coupling simulation methods could be explored to further investigate its rheological properties.

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